Off on a Comet

Chapter XXXII

In which the professor and his students juggle with sextillions,
quintillions and other multiples of billions

A quarter of an hour later, the visitors to the
Hansa had reassembled in the common hall of Nina’s Hive.

“Now, gentlemen, we can proceed,” said the professor. “May I request that
this table may be cleared?”

Ben Zoof removed the various articles that were lying on the table, and
the coins which had just been borrowed from the Jew were placed upon it
in three piles, according to their value.

The professor commenced. “Since none of you gentlemen, at the time of the
shock, took the precaution to save either a metre measure or a kilogram
weight from the Earth, and since both these articles are necessary for
the calculation on which we are engaged, I have been obliged to devise
means of my own to replace them.”

This exordium delivered, he paused and seemed to watch its effect upon
his audience, who, however, were too well acquainted with the professor’s
temper to make any attempt to exonerate themselves from the rebuke of
carelessness, and submitted silently to the implied reproach.

“I have taken pains,” he continued, “to satisfy myself that these coins
are in proper condition for my purpose. I find them unworn and unchipped;
indeed, they are almost new. They have been hoarded instead of
circulated; accordingly, they are fit to be utilized for my purpose of
obtaining the precise length of a terrestrial metre.”

Ben Zoof looked on in perplexity, regarding the lecturer with much the
same curiosity as he would have watched the performances of a travelling
mountebank at a fair in Montmartre; but Servadac and his two friends had
already divined the professor’s meaning. They knew that French coinage is
all decimal, the franc being the standard of which the other coins,
whether gold, silver, or copper, are multiples or measures; they knew,
too, that the calibre or diameter of each piece of money is rigorously
determined by law.

Having undertaken the following calculations on a piece of paper, the
Professor presented them to his audience.

10 pieces

of 5 francs

at 0.037 m =

0.370 m

10 "

of 2 "

at 0.027 m =

0.270 m

20 "

of 50 cent,

at 0.018 m =

0.360 m

TOTAL

……

1.000 m

“Excellent, Professor,” said Hector Servadac. “All that remains is to lay
out these forty coins with a straight light through their respective
centres, and we will have the exact dimensions of a terrestrial metre.”

“By the name of Kabyle!” cried Ben Zoof. “All the same, it’s grand being
a scientist.”

“He calls that being a scientist!” retorted Palmyrin Rosette, shrugging
his shoulders.

The ten five-franc pieces were laid flat on the table, and placed one
next to the other in such a manner that their centres lay along a
straight line; and then the ten ten-franc pieces, and then the twenty
fifty-centime coins. A mark on the table indicated the extent of the line
so formed.

“Gentlemen, there you have it,” said the Professor. “An exact terrestrial
metre.”

The measurement thus obtained was by means of a pair of compasses divided
accurately into ten equal portions, or decimetres, each of course 3.93
inches long. A lath was then cut of this exact length and given to the
engineer of the Dobryna, who was directed to cut out of the solid
rock the cubic decimetre required by the professor.

The next business was to obtain the precise weight of a kilogram. This
was by no means a difficult matter. Not only the diameters, but also the
weights, of the French coins are rigidly determined by law, and as the
silver five-franc pieces always weigh exactly twenty-five grams, the
united weight of forty of these coins is known to amount to one kilogram.

“Oh!” cried Ben Zoof; “to be able to do all this I see you must be rich
as well as learned.”

With a good-natured laugh at the orderly’s remark, the meeting adjourned
for a few hours. By the appointed time the engineer had finished his
task, and with all due care had prepared a cubic decimetre of the
material of the comet.

“Now, gentlemen,” said Professor Rosette, “we are in a position to
complete our calculation; we can now arrive at Gallia’s attraction,
density, and mass.”

Everyone gave him his complete attention.

“Before I proceed,” he resumed, “I must recall to your minds Newton’s
general law, ‘that the attraction of two bodies is directly proportional
to the product of their masses, and inversely proportional to the square
of their distances.’”

“Yes,” said Servadac; “we remember that.”

“Well, then,” continued the professor, “keep it in mind for a few minutes
now. Look here! In this bag are forty five-franc pieces—altogether they
weigh exactly a kilogram; by which I mean that if we were on the Earth,
and I were to hang the bag on the hook of the spring balance, the
indicator on the dial would register one kilogram. This is clear enough,
I suppose?”

As he spoke the professor designedly kept his eyes fixed upon Ben Zoof.
He was avowedly following the example of Arago, who was accustomed always
in lecturing to watch the countenance of the least intelligent of his
audience, and when he felt that he had made his meaning clear to him, he
concluded that he must have succeeded with all the rest. In this case,
however, it was technical ignorance, rather than any lack of
intelligence, that justified the selection of the orderly for this
special attention.

Satisfied with his scrutiny of Ben Zoof’s face, the professor went on.
“And now, gentlemen, we have to see what these coins weigh here upon
Gallia.”

He suspended the money bag to the hook; the needle oscillated, and
stopped. “Read it off!” he said.

The weight registered was one hundred and thirty-three grams.

“There, gentlemen, one hundred and thirty-three grams! Less than
one-seventh of a kilogram! You see, consequently, that the force of
gravity here on Gallia is not one-seventh of what it is upon the Earth!”

“Interesting!” cried Servadac, “most interesting! But let us go on and
compute the mass.”

“No, captain, the density first,” said Rosette.

“Certainly,” said the lieutenant; “for, as we already know the volume, we
can determine the mass as soon as we have ascertained the density.”

The professor took up the cube of rock. “You know what this is,” he went
on to say. “You know, gentlemen, that this block is a cube hewn from the
substance of which everywhere, all throughout your voyage of
circumnavigation, you found Gallia to be composed—a substance to which
your geological attainments did not suffice to assign a name.”

“Our curiosity will be gratified,” said Servadac, “if you will enlighten
our ignorance.”

But Rosette did not take the slightest notice of the interruption.

“A substance it is which no doubt constitutes the sole material of the
comet, extending from its surface to its innermost depths. The
probability is that it would be so; your experience confirms that
probability: you have found no trace of any other substance. Of this rock
here is a solid decimetre; let us get at its weight, and we shall have
the key which will unlock the problem of the whole weight of Gallia. We
have demonstrated that the force of attraction here is only one-seventh
of what it is upon the Earth, and shall consequently have to multiply the
apparent weight of our cube by seven, in order to ascertain its proper
weight. Do you understand me, goggleeyes?”

This was addressed to Ben Zoof, who was staring hard at him. “No!” said
Ben Zoof.

“I thought not; it is of no use waiting for your puzzle-brains to make it
out. I must talk to those who can understand.”

The professor took the cube, and, on attaching it to the hook of the
spring balance, found that its apparent weight was one kilogram and four
hundred and thirty grams.

“Here it is, gentlemen; one kilogram, four hundred and thirty grams.
Multiply that by seven; the product is, as nearly as possible, ten
kilograms. What, therefore, is our conclusion? Why, that the density of
Gallia is just about double the density of the Earth, which we know is
only five kilograms to a cubic decimetre. Had it not been for this
greater density, the attraction of Gallia would only have been
one-fifteenth instead of one-seventh of the terrestrial attraction.”

The professor could not refrain from exhibiting his gratification that,
however inferior in volume, in density, at least, his comet had the
advantage over the Earth.

Nothing further now remained than to apply the investigations thus
finished to the determining of the mass or weight. This was a matter of
little labour.

“Let me see,” said the captain; “what is the force of gravity upon the
various planets?”

“You can’t mean, Servadac, that you have forgotten that? But you always
were a disappointing pupil.”

The captain could not help himself: he was forced to confess that his
memory had failed him.

“Well, then,” said the professor, “I must remind you. Taking the
attraction on the Earth as 1, that on Mercury is 1.15, on Venus it is
0.92, on Mars 0.5, and on Jupiter 2.45; on the moon the attraction is
0.16, whilst on the surface of the sun a terrestrial kilogram would weigh
28 kilograms.”

“Therefore, if a man upon the surface of the sun were to fall down, he
would have considerable difficulty in getting up again. A cannon ball,
too, would only fly a few yards,” said Lieutenant Procope.

“A jolly battle-field for cowards!” exclaimed Ben Zoof.

“Not so jolly, Ben Zoof, as you fancy,” said his master; “the cowards
would be too heavy to run away.”

Ben Zoof ventured the remark that, as the smallness of Gallia secured to
its inhabitants such an increase of strength and agility, he was almost
sorry that it had not been a little smaller still.

“Though it could not anyhow have been very much smaller,” he added,
looking slyly at the professor.

“Idiot!” exclaimed Rosette. “Your head is too light already; a puff of
wind would blow it away.”

“I must take care of my head, then, and hold it on,” replied the
irrepressible orderly.

Unable to get the last word, the professor was about to retire, when
Servadac detained him.

“Permit me to ask you one more question,” he said. “Can you tell me what
is the nature of the soil of Gallia?”

“Yes, I can answer that. And in this matter I do not think your
impertinent orderly will venture to put Montmartre into the comparison.
This soil is of a substance not unknown upon the Earth.” And speaking
very slowly, the professor said: “It contains seventy per cent
tellurium…”